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size remains fixed. The maximum variation of gray values as well as the 
significance of the channel-specific mean value functions increase as the 
area size decreases. 
The position-dependence of the recording becomes also apparent in the di- 
rect comparison of the various area-size-dependent mean value functions: 
The reduction of the size of the test areas results, as expected, in a 
refined representation of local influences (cf. fig. 3,4) whereas an ex- 
pansion leads to their suppression (cf. fig. 5,2). 
The causes for the position-dependence of the mean gray values are not 
treated here. Taken into account are systematic variations of object prop- 
erties (water), of the atmosphere, as well as the measuring system. 
Hence it follows that areas of homogenous land cover are not always imaged 
with homogenous gray values. The present example rather displays - depend- 
ing on the size of the test area - a markedly ^ pósition-dependent dis- 
tribution of gray values. 
4.2 Eigenvalues 
The n eigenvalues of the Q-matrix define the length of the semimajor 
axes of n-dimensional error ellipsoids [1], and hence their form. Now the 
assumption suggests itself that every land cover type has its unique and 
typical eigenvalues which allow its unambiguous distinction from the 
multispectrally adjacent land cover type. However, this is valid only if 
it can be verified that the eigenvalues are independent of position and 
size of the test area. The results (fig. 5, 6, 7) disprove this: 
- The distribution of the largest eigenvalue A, across all subareas 
shows, independent of the area size, a nerkedl y systematic position- 
dependent behavior. 
- Differences in the position-dependent distribution of M» result as a 
refinement of the function as the area size decreases. 
- For the remaining eigenvalues A,, X5, À position-dependence could 
Le 2:63 4 
not be verified. 
- The sensor-specific width of the error margin decreases with 
decreasing eigenvalues. 
- The maximum change of eigenvalue A, and the width of the error margin 
reaches its minimum at a test area size of 100 x 96 pixels. 
4.3 Eigenvectors 
The discrimination of two adjacent land-cover-dependent clusters is unique- 
ly defined if, apart from the form, the orientation of the error ellipsoids 
is stable as well, i.e. independent of both the position and the size of 
the test area. With interpenetrating ellipsoids this becomes more  com- 
plicated to the degree in which their relative orientation changes. As the 
change in direction of the largest semimajor axis has the strongest effect 
in this case, the investigation will focus on it in the following. 
The computation results now demonstrate in detail that the sensor-dependent 
uncertainty in orientation increases with decreasing test area size (fig.8, 
9,10):The variation of orientation is as low as approx. 59 for an area 
175